The Difference Between GCF and LCM

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**Avebury, Robin Heath, Cerrig Duon** submitted by Andy B : 19th July 1997, the last big Ley Hunter Moot. Robin Heath demonstrates the astronomical and geometrical knowledge built into megalithic sites, suggesting reasons as to why the history hooks refuse admission of this rnaterial at present. His fully illustrated talk was augmented by models and years of experience in megalithic achitecture. soli-lunar astronomy and as a lecturer in adult education. In... (Vote or comment on this photo)

What is GCF? GCF stands for “greatest common factor”. The greatest whole number that can divide a given number into two or more equal parts is defined as the greatest common factor (GCF). This number can be a factor of two or more whole numbers. We can define factors as digits which, when multiplied, give the number itself. When a factor is shared by two or more given numbers, it can be referred to as a common factor. The GCF is also called Greatest Common Divisor (GCD) or Highest Common Factor (HCF).

Here we will be looking at the best methods to calculate greatest common factor (GCF).

1. Listing Method

The first step is to list out all the factors of the given numbers. The next step is to find the factor that is common to all the given numbers. The greatest factor that is common to all numbers becomes the GCF. Thus, If we find the common factors of two numbers, the greatest common factor can be produced from the list of these factors.
Example: Say we have to find the GCF of 4, 16 using the listing method.

Factors of 4 = 1,4
Factors of 16 = 1, 2, 4, 8, 16.
Common Factors of 4, 16 = 1, 4.

As 4 is the greater number thus, 4 is the GCF of 4 and 16.

2. Prime Factorisation Method

Listing all the factors can be very time-consuming, primarily if we deal with large numbers. In such a case, it is easier to find the prime factors of the numbers to find the GCF. In this method, the first thing to do is list all the prime factors of each number. The next step is to find all the common prime factors. By multiplying these common prime factors, the resulting number is the GCF of the two numbers.
Example: We have to find the GCF of 4, 16 using the prime factors method

Prime Factors of 4 = 2 × 2
Prime Factors of 16 = 2 × 2 × 2 × 2
Common Prime Factors = 2 × 2

Thus, GCF is 4

What is LCM?

The full form of LCM is Least or Lowest Common Multiple. It can be defined as the lowest common multiple that is divisible by the given set of natural numbers. The LCM has to be a multiple of all the given numbers. Thus, the LCM of the numbers is the smallest number that appears as a multiple and can be divided by the given numbers.

Methods to Calculate LCM

1. Listing Method

In this method, we make a list of all the multiples belonging to the given set of numbers. The smallest multiple, which is common to all numbers, provide us with the LCM.
Example: To find the LCM of 4, 16 using the listing method

Multiples of 4: 4, 8, 12, 16, 20, 24 …..
Multiples of 16: 16, 32, 48 ….
LCM: 16

2. Prime Factorisation Method

To find the LCM using this method, we first write all the numbers as a product of their prime factors. We then write down all the prime factors making sure that the common factors are listed only once. By multiplying these, we get the LCM.
Example: LCM of 4, 16 using the prime factors method is 16

Prime Factors of 16 = 2 × 2 × 2 × 2
Thus, LCM = 2 × 2 × 2 × 2 = 16

Conclusion

The best way to study this topic is by availing a reliable institution such as Cuemath. At Cuemath, the certified tutors use several resources to deliver an impactful lecture while combining fun with learning. A student can work at his own pace allowing him to confidently master topics and attain success.

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